Vault Service account, all enterprise vault services run under VSA. SQL authentication/Windows authentication/Exchange authentication are all done using VSA credentials

System Mailbox are used by various tasks configured in EV environment against exchange servers to create MAPI threads/sessions. These sessions are required for archiving data from exchange to enterprise vault.

So the relation can be "put in statement" as Enterprise vault logs in to Exchange using VSA credentials and once authenticated, it opens connection using system mailbox(es).

Apart from above, if:

Any issue with vault service account will cause EV to shutdown completely as all authentication will fail etc.

Any issue with system mailbox will stop EV from creating / opening connections with Exchange and hence will stop archiving or mark the task to failed state as per the scenario.